(a) Overall objective: Design a water tank that will hold a volume of water V =
ID: 1712868 • Letter: #
Question
(a) Overall objective: Design a water tank that will hold a volume of water
V = 5.00 x 105 liters = 500 m3at the lowest cost.
(b) Brainstorm, gather information. Hint: keep it simple. Work with the geometries you are familiar with. You do not need to try ‘crazy’ tank geometries. (20x20x20) Record all your ideas.
(c) Construction costs:
$250 /m2 for flat surface,
$300/m2 for cylindrical surface and
$400/m2 for spherical surface.
(d) Formulas:
Volume of cylinder, Vc =r2h,
Volume of sphere, Vh = (4/3)r3,
surface area of cylinder (no base or lid), Sc = 2rh,
surface area of sphere, Sh = 4r2.
Also 1m3 = 1000 L.
Discuss all the different shapes you considered, as well as the process you followed to select the cheapest alternative.
Show all calculations for your selected alternative.
Explanation / Answer
Since the cost is minimum for flat surface construction, we should go for a cylinderical tank with lesser height and greater dia.
On calculating the volume by trial and error method, we find the following dimensions for the tank
Radius - 7m
Height - 3.248m
Volume of the tank = r2h = 3.14*7*7*3.248 = 499.99 ~= 500 m3
Hence, the construction cost will be
1) Flat surface r2
Cost = $ 250 / m2
2) Cyliderical surface 2rh
Cost = $ 300 / m2
Total Cost = 250*r2 + 300*2rh = $ 81340 approximately
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